Pythagorean Word Problems in Real Life

Pythagorean Word Problems in Real Life

Learning Objective

At the end of the lesson, you will be able to apply the Pythagorean theorem to solve real-life word problems.

Introduce the learning objective of the lesson to the students.

What do you already know about Pythagorean theorem?

What is the Pythagorean Theorem?

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Explain the Pythagorean theorem to the students and provide an example.

Example 1

A ladder is leaning against a wall. The base of the ladder is 6 feet away from the wall and the ladder is 10 feet long. How high up the wall does the ladder reach?

Ask the students to solve the problem using the Pythagorean theorem.

Example 2

A rectangular field is 60 feet by 80 feet. What is the length of the diagonal?

Ask the students to solve the problem using the Pythagorean theorem.

Example 3

A right triangle has a hypotenuse of 17 cm and one leg of 8 cm. What is the length of the other leg?

Ask the students to solve the problem using the Pythagorean theorem.

Example 4

A kite is flying on a string that is 200 meters long. If the string makes an angle of 60 degrees with the ground, how high is the kite above the ground?

Ask the students to draw a diagram and solve the problem using the Pythagorean theorem.

Example 5

A person walks 6 km due east and then 8 km due north. How far is the person from the starting point?

Ask the students to draw a diagram and solve the problem using the Pythagorean theorem.

Challenge Problem

A tree casts a shadow that is 20 feet long. At the same time, a 6-foot-tall man standing near the tree casts a shadow that is 4 feet long. How tall is the tree?

Ask the students to draw a diagram and use the Pythagorean theorem to solve the problem. This problem requires the use of similar triangles.

Write down 3 things you learned in this lesson.

Have students enter three things they learned in this lesson. With this they can indicate their own learning efficiency of this lesson.

Write down 2 things you want to know more about.

Here, students enter two things they would like to know more about. This not only increases involvement, but also gives them more ownership.

Ask 1 question about something you haven't quite understood yet.

The students indicate here (in question form) with which part of the material they still have difficulty. For the teacher, this not only provides insight into the extent to which the students understand/master the material, but also a good starting point for the next lesson.